decompwlj 3D

Primes congruent to 21 mod 31

A142025 on the OEIS · family primes

Weight–level plate of Primes congruent to 21 mod 31
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA142025 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L48,133 · 48.13 %
Weight class, k ≤ L51,865 · 51.87 %
Ties, k = L0
On the level line L = 16,328
Forced level, l ≤ d²741
Range of a(n)83 … 49,947,221
Range of the jump d62 … 4,464
Largest weight k, level L49,946,167, 791,389

66 different gaps occur, from 62 to 4,464; the level share is 48.13 %; there are no ties.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.